Implicit differentiation to find the length of a spiral

Hey,

I was wondering if there was a quicker/better way of working this out:

x(t)=(t+a)cos(t), y(t)=(t+a)sin(t)

therefore dx/dt= -(t+a)sin(t) + acos(t)

and dy/dt= (t+a)cos(t) + asin(t)

To work out the length I would have to use L=int{sqrt(1+ [dy/dx]^2 )}

EDIT: forgot about the integral :D

[dy/dx]^2 is a nightmare to work out

do I have to crunch the numbers or is there a way to simplify and do it quicker?

Thanks in advance

EDIT: Oh.. and this is called parametric differentiation :S